The human experience of color is dependent on the spectral properties of the stimulant, i.e. the color being observed, combined with the spectral sensitivities of the eye+brain system. This in turn is governed by the spectral sensitivities of the LMS (long, medium, short wavelength) cones residing in the retina and the neural and cognitive processing of the LMS responses performed by the retina and brain. Thus, whereas measuring the spectra of a color stimulant is objective and unambiguous, measuring the human sensation known as color is dependent on the validity of what are referred to as the human observer functions CIEXYZ (which define color matching and can be related to LMS) and the calculation for CIELAB (which is dependent on XYZ and defines how colors are perceived).
Since CIEXYZ and CIELAB are derived from experiments involving human observers, the validity of CIEXYZ and CIELAB may be compromised by errors in the experimental data acquired (in the case of color matching experiments), errors in the methods used to convert the raw data to human observer functions, and errors in color order systems such as Munsell which were used to optimize the calculation for CIELAB.
The imperfections in CIEXYZ and CIELAB are well-known in the industry:                a) Colors that measure the same values of CIEXYZ and CIELAB do not necessarily match, especially whites comprised of significantly different spectra.        b) Colors that differ by the same Euclidean distance in CIELAB may appear nearly identical or may appear dramatically different depending on the location of the colors within the CIELAB coordinate system and the direction of their color difference.        
If the current methods for calculating CIEXYZ and CIELAB were valid, colors with significantly different spectra but similar values of CIEXYZ and CIELAB would match visually. Such pairs of colors are called “metameric pairs” or “metamers”. To the extant that such pairs of colors do not match visually, one can say that CIEXYZ and CIELAB are imperfect methods for defining or measuring color. This results in pairs of colors that are metameric matches numerically but not visually.
In order to identify possible sources of error in the definitions of CIEXYZ and CIELAB, we begin with a very brief history of modern day colorimetry. The Commission Internationale de l'Éclairage (hereinafter “CIE”) XYZ observer functions are the basis for most color measurements that require the matching of colors. By combining these functions with non-linear color appearance models (CAMs) such as CIELAB and CIECAM96s CAMs, complex color images as well as simple color patches can be reproduced with great success if the color media are similar in spectral behavior.
The color matching functions of the CIE 1931 standard were based on the data of Guild using seven observers and Wright using ten observers together with the CIE 1924 luminous efficiency function V (λ). As a result of visual vs. numerical discrepancies in the matching of paper white, Stiles performed a “pilot” repeat of the 1931 determination of the color matching functions using 10 observers and (together with Burch) a “final” version using 49 observers in 1958. This latter “final” experiment was performed using a larger field of view (10 degree rather than 2 degree) and hence the two standards from 1931 and 1958 are referred to as the 2 and 10-degree observer, respectively. Example plots of the raw color matching data acquired from the multiple observers by Stiles and Burch, N.P.L. colour-matching investigation: Final Report (1958), National Physical Laboratory, pp. 1-26, clearly indicate significant noise and variability in the data, probably due to the procedures used to obtain the color matches and the imperfect skill of the participants in the art of adjusting colors for purposes of obtaining a match.
In his book “The Reproduction of Colour” pp. 138-141 and pp. 706-707, Robert Hunt relates the historical XYZ observer functions to the spectral sensitivities of the LMS cones in the retina. Hunt cites Estevez and similar references regarding the red, green, blue spectral sensitivities of the cones (p. 706). By comparing these estimates with the existing XYZ observer functions, Hunt defines the Hunt-Estevez-Pointer conversion that converts the XYZ observer functions to the long-medium-short spectral sensitivities of the eye LMS (as defined in most references) or equivalently ρ, β, γ (the labels Hunt prefers to avoid confusion with other color values such as using “L” for luminance). The Hunt-Estevez-Pointer matrix is defined as:
                              M                      XYZ            ->            LMS                          =                  (                                                    0.38971                                            0.68898                                                              -                  0.07868                                                                                                      -                  0.22981                                                            1.18340                                            0.04641                                                                    0                                            0                                            1.00                                              )                                    Eq        .                                  ⁢                  (                      1            ⁢                          -                        ⁢            1                    )                    
While the CIEXYZ observer functions appear to work well between media that are somewhat similar using similar lighting conditions, there appears to be a discrepancy between measurement and visual matches for media with radically different spectra, particularly in the areas of whites. This discrepancy has been documented as the impetus for the 10 degree (vs. 2 degree) observer function effort performed by Stiles and Burch from 1955-1958 (Interim Report to the Commission of Internationale de l'Eclariage, Zurich, 1955, on the National Physical Laboratory's investigation of colour-matching (1955), pp. 168-181; and N.P.L. colour-matching investigation: Final Report (1958), National Physical Laboratory, pp. 1-26) and is the basis for the deviation from standard CIE XYZ metrology developed in conjunction with MATCHPRINT™ Virtual technology from Eastman Kodak, which is used in a variety of systems that require an accurate visual color match between displays and printed images viewed under standard illumination.
The methods used to improve the CIE functions fall into two categories. The first category are methods such as those used by Thornton (1998) and also by Matsushiro, Ohta, Shaw, and Fairchild (Optimizing Color-Matching Functions for Individual Observers Using a Variation Method, Journal of Imaging Science and Technology, Vol. 45, No. 5, September/October 2001, pp. 472-480) which attempt to alter the human observer functions on a wavelength by wavelength basis, possibly with constraints, in order to minimize error between metameric pairs as well as to remain similar to the original human observer functions. This effectively allows the number of adjustable parameters to be 3×32=96 or higher.
The second category of approach is to use a small number of parameters as discussed in Fairchild (A Novel Method for the Determination of Color Matching Functions, COLOR research and application, 1989, pp. 122-130) and North and Fairchild (Measuring Color-Matching Functions. Part I, Vol. 18, No. 3, June, 1993 op. 155-162; and Measuring Color-Matching Functions, Part II, New Data for Assessing Observer Metamerism, Vol. 18, No. 3, June, 1993, pp. 163-170) relying for example on the “deviant observer” which attempts to account for yellowing effects of aging due to the lens and the macula by applying broad band absorption spectra to the LMS functions. This approach has the deficiency of being very limited in how it modifies the standard human observer functions. So although this approach can accurately mimic the standard human observer functions, it cannot adequately modify the functions in order to reduce the calculated ΔE errors between metameric pairs that have significantly different spectra and yet match visually.